Scientific Notation Calculator
Convert numbers and perform calculations in scientific notation
Scientific Notation Calculator
Convert numbers to scientific notation, E-notation, and engineering notation. Perform arithmetic operations with numbers in scientific notation format.
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🔄 Scientific Notation Converter
Provide a number below to get its scientific notation, E-notation, engineering notation, and real number format. It accepts numbers in the following formats 3672.2, 2.3e11, or 3.5x10^-12.
📊 Conversion Results
Enter a number above and click "Convert" to see the results.
🧮 Scientific Notation Calculator
Use the calculator below to perform calculations using scientific notation.
Calculation Result
Select an operation above to see the calculation results.
📚 Understanding Scientific Notation
Scientific notation
Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write and perform calculations with. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations. In scientific notation, numbers are written as a base, b, referred to as the significand, multiplied by 10 raised to an integer exponent, n, which is referred to as the order of magnitude:
b × 10n
Below are some examples of numbers written in decimal notation compared to scientific notation:
| Decimal notation | Scientific notation |
|---|---|
| 5 | 5 × 100 |
| 700 | 7 × 102 |
| 1,000,000 | 1 × 106 |
| 0.0004212 | 4.212 × 10-4 |
| -5,000,000,000 | -5 × 109 |
E-notation
E-notation is almost the same as scientific notation except that the "× 10" in scientific notation is replaced with just "E." It is used in cases where the exponent cannot be conveniently displayed. It is written as:
bEn
where b is the base, E indicates "x 10" and the n is written after the E. Below is a comparison of scientific notation and E-notation:
| Scientific notation | E-notation |
|---|---|
| 5 × 100 | 5E0 |
| 7 × 102 | 7E2 |
| 1 × 106 | 1E6 |
| 4.212 × 10-4 | 4.212E-4 |
| -5 × 109 | -5E9 |
The "E" can also be written as "e" which is what is used by this calculator. It can also be written in other ways depending on the context, such as being represented differently in different programming languages.
Engineering notation
Engineering notation is similar to scientific notation except that the exponent, n, is restricted to multiples of 3 such as: 0, 3, 6, 9, 12, -3, -6, etc. This is so that the numbers align with SI prefixes and can be read as such. For example, 103 would have the kilo prefix, 106 would have the mega prefix, and 109 would have the giga prefix. Note that the decimal place of the number can be moved to convert scientific notation into engineering notation. For example:
1.234 × 108 (scientific notation)
can be converted to:
123.4 × 106 (engineering notation)